Does the Constant Speed of Light Postulate Extend to Mechanical Processes?

[JM]

Question: Does the Postulate of Constant Light Speed apply also to mechanical processes? For example, is a cannonball or a sound wave required to move at the same speed independent of the motion of the "emitting" or "recieving" body? If so, what is the reasoning that leads to this requirement? If not, cannot a mechanical clock be built whose rate of ticking is independent of its motion? The objection that such a clock would allow speed to be determined appears invalid, because the speed calculated would be the relative speed of the two observers.

 

[JesseM]

Question: Does the Postulate of Constant Light Speed apply also to mechanical processes?

Depends what you mean by this. All mechanical processes can be understood in terms of electromagnetic interactions between the atoms that make up the object, so mechanical clocks should show the same sort of time dilation as light clocks (anyway, the other postulate of relativity is that all laws of physics should work the same way in different reference frames, which means that all clocks should show time dilation in the same way).

For example, is a cannonball or a sound wave required to move at the same speed independent of the motion of the "emitting" or "recieving" body?

Not for a cannonball, although for any wave in a medium the speed of the wave should be constant in the rest frame of the medium, regardless of the speed of the emitter (but for any sublight wave, the speed of the wave will be different in different reference frames).

If not, cannot a mechanical clock be built whose rate of ticking is independent of its motion?

I don't follow your reasoning--how could the fact that a cannonball's speed depends on the speed of the cannon be used to build a clock whose rate of ticking is independent of motion, for example?

 

[JM]

OK. Let's build a sound clock on the same plan as the famous light clock. The Light Postulate will not apply, but as you said the speed of the sound wave will be different in each frame. Let's do the calculation and see if the rate of ticking is the same in the "moving" frame and as perceived in the "rest" frame.

 

[pervect]

OK. Let's build a sound clock on the same plan as the famous light clock. The Light Postulate will not apply, but as you said the speed of the sound wave will be different in each frame. Let's do the calculation and see if the rate of ticking is the same in the "moving" frame and as perceived in the "rest" frame.

We already know it will keep the same time because there isn't any way of detecting absolute motion by measuring clocks in boxes.

However, if you'd care to specify a little more about how you envisoned your clock working, we could give more details.

 

[JesseM]

OK. Let's build a sound clock on the same plan as the famous light clock. The Light Postulate will not apply, but as you said the speed of the sound wave will be different in each frame. Let's do the calculation and see if the rate of ticking is the same in the "moving" frame and as perceived in the "rest" frame.

The speed of a given sound wave will be different in each frame, but if you have a box filled with a medium such as air, with the medium at rest with respect to its box, then an observer inside the box will see the "sound clock" in his own box work the same way regardless of how fast the box is moving relative to any other landmark in the universe such as the galaxy. And if you have two such boxes moving with respect to each other, then each observer will see the other observer's "sound clock" slowed down in a precisely symmetrical way. Because of this perfect symmetry, there's no way you can use these sound clocks to pick out any sort of preferred frame. This is just a necessary consequence of the basic postulate of relativity which says all laws of physics must work the same way in all inertial frames, which means any experiment you do in a box moving inertially should be observed to have the same outcome regardless of how fast the box is moving relative to external landmarks.

 

[JM]

And if you have two such boxes moving with respect to each other, then each observer will see the other observer's "sound clock" slowed down in a precisely symmetrical way. The question now is why will an observer see the other observers sound clock slowed down? The slowing down of the light clock is due to the light postulate, but the sound clock is not required to obey the postulate.

 

[Ich]

The sound clock in your Gedankenexperiment could do whatever it wants: If you assume Euclidean space you wou conclude that it does not slow down. If you assume Minkowski spacetime, it would slow down just as JesseM described. So you learn nothing.
The tricky point is: You can derive that light clocks would slow down. If a sound clock would behave otherwise, you could tell from the difference whether you are moving or not. When you accept the relativity postulate, you know that this cannot be true. So you can deduce that a sound clock would also slow down, as every other physical process.
That's why the light clock Gedankenexperiment is useful and reveals much more than the behaviour of some special apparatus.

 

[robphy]

And if you have two such boxes moving with respect to each other, then each observer will see the other observer's "sound clock" slowed down in a precisely symmetrical way.
The question now is why will an observer see the other observers sound clock slowed down? The slowing down of the light clock is due to the light postulate, but the sound clock is not required to obey the postulate.

The sound clock (and any other clock) carried by an inertial observer will tick identically with that observer's light clock, or else (as pointed out by others) one can use this to distinguish inertial states of motion. According to relativity, the slowing down of all clocks is due to [better: implied by] the light postulate... it's just that the light clock is easier to analyze because of the property that the speed of light (but not the speed of sound or the speed of a superball) is the same for all inertial observers. (Under a boost, the velocity transformation doesn't change the speed of light.) When I have some free time [which won't be anytime soon], I was going to explicitly work out the geometry and SR-kinematics of the sound clock and the superball clock [as I have done for the light clock].

 

[JesseM]

The question now is why will an observer see the other observers sound clock slowed down? The slowing down of the light clock is due to the light postulate, but the sound clock is not required to obey the postulate.

Remember, there are two basic postulates of special relativity--one is the light postulate, but the other is the postulate that all laws of physics should work the same way in different inertial reference frames. Anyway, sound waves are based entirely on electromagnetic interactions between the molecules that make up the medium, so the light postulate alone is probably enough to show that sound waves should behave the same way in the different inertial frames defined by the Lorentz transformation of SR.

 

[JM]

Review of the advices posted here and related literature leads to the following understanding.
Consider astronaut A coasting in deep space. He has a light clock and a mechanical clock. These clocks always agree. The ticking rate of the clocks do not change with time, as long as the length of the light clock is constant and it remains at rest. The rates of these clocks are not affected by the presence or absence of astronaut B, or by his observation of A's clocks. ( See Taylor and Wheeler, p. 76 )
So along comes astronaut B who notices flashing lights on A's ship. He observes the zigzag motion of the light and measures the distance from up-peak to down-peak and the time between down-peaks. He interprets this as a light clock and refers to his book of formulas, where he finds:
t' ( B ) = t (A ) / sq rt ( 1 - v*v/ c*c )

From here B has two options. If he knows his speed v relative to A he can calculate A's clock rate. If he doesn't know his speed he can adjust the length of his own light clock so it agrees with the peak-to-peak length of the zigzag, which is the length of A's clock. The two light clocks then agree ( see Feynman, "Six Not-so-Easy Pieces", p 59 ). Then B can use his t ( at rest ) as A's t in the formula to calculate his speed v relative to A.
Because neither A's clocks nor B's clocks are affecte by these obervations, the slowing represented by the formula can be considered an optical effect ( image ) caused by geometry and the Light Postulate.
Since the mechanical clocks agree with their respctive light clocks, and the light clocks agree with each other , the mechanical clocks must also agree with each other. So the question is whether there is an apparent slowing of the mechanical clock, and if so, why?
Comments?

 

[JesseM]

From here B has two options. If he knows his speed v relative to A he can calculate A's clock rate.

He can only calculate A's "clock rate" relative to a particular frame, there is no objective truth about what A's clock rate "really" is in some frame-independent sense.

If he doesn't know his speed he can adjust the length of his own light clock so it agrees with the peak-to-peak length of the zigzag, which is the length of A's clock.

But then his clock will no longer be ticking at the correct rate as seen by himself! If the length had originally been set up so that the light would bounce between the two mirrors in 1 second, then by changing the distance between the mirrors, the light will no longer take 1 second (as measured by mechanical clocks, biological clocks, or any other type of clock at rest in his frame) to bounce between the mirrors.

And in any case, even if B adjusts the distance so that the light takes the same time to bounce between his mirrors as it does to bounce between A's mirrors in B's own frame, this does not mean that both clocks will tick at the same rate in A's frame. A and B do not agree on the ratio between ticks of their unadjusted clocks--A sees B's clock running slower than his own, while B sees A's clock running slower than his own. So if B extends the length between his mirrors to slow down the ticking rate of his own clock, this will bring his clock's ticking rate closer to A's in his frame, but since A already saw B's clock ticking slow in A's frame, this means that in A's frame B will be making the difference between their clocks even greater by extending the length between the mirrors.

Because neither A's clocks nor B's clocks are affecte by these obervations, the slowing represented by the formula can be considered an optical effect ( image ) caused by geometry and the Light Postulate.

No, it can't be considered an optical effect. If they travel apart and then reunite, their will be a real age difference between them--that's the so-called twin paradox. Also, I don't understand what you mean when you say "neither A's clocks nor B's clocks are affected by these observations"--you had B changing the ticking rate of his own light clock so that it was no longer in sync with his other clocks, surely that is something that "affects" his light-clock, not a mere passive "observation".

Since the mechanical clocks agree with their respctive light clocks

Not if you change the distance between the mirrors! The light clock only ticks at the correct rate if you have the correct distance--for example, if I want the light to go from the bottom mirror to the top and back to the bottom every second, the distance between the mirrors must be half a light-second in my frame.

 

[bernhard.rothenstein]

A machine gun that fires successive bullets , at constant time intervals is a very good clock. If two inertial observers in relative motion are equipped with identical machine guns at rest relative to them then they detect the same period as long they measure the perods of theirs own clocks. Comparing the period of his own clock with the period of the clock of the other observer the two time intervals could be related by the time dilation formula or by the Doppler shift formula. In the first case one of them measures a nonproper time
interval the second a proper time interval. In the case of the Doppler effect both of them measure poper time intervals.

 

[JM]

He can only calculate A's "clock rate" relative to a particular frame, there is no objective truth about what A's clock rate "really" is in some frame-independent sense.

JesseM: What is the point of this comment?
The light clock has been described in the literature more than once. The meaning of " A's clock rate" is pretty clearly the rate of A's clock as seen by A who is at rest with respect to his clock, that's the particular frame.

 

[JesseM]

JesseM: What is the point of this comment?
The light clock has been described in the literature more than once. The meaning of " A's clock rate" is pretty clearly the rate of A's clock as seen by A who is at rest with respect to his clock, that's the particular frame.

It wasn't clear with me you were agreeing there was no frame-independent truth about the clock rate, though, since your original post seemed to be suggesting we could identify a preferred frame using a sound wave clock, and your later post suggested the slowing of clocks was just an "optical effect". And if you understood the standard meaning of a light clock in the literature, why did you suggest changing the distance between the mirrors, yet still defining the observer's "clock rate" in terms of such an altered clock (which would no longer agree with other types of clocks at rest in the observer's frame)?

 

[russ_watters]

Shall we through a monkey wrench in this and add an aether (since it is relevant to the "light clock", it should probably be addressed with the "sound clock")? One of the points of a light clock is that if there were an aether, it would affect the operation of the light clock. The same goes for the "sound clock": if the "sound clock" is open (air flowing through it), then the motion of the clock through the stationary air likely will affect it's operation.

 

[JM]

JesseM: Thanks for your quick reply. I do agree with the analysis of the light clock, but its the conclusions that are a problem. What I'm trying to do is make sense of the various statements, sometimes apparently controdictory, about SR. I agree with the idea that there is no place of absolute rest, and no time of absolute zero, though the age of the universe poses a question. With this in mind, what would a preferred frame be? In view of Taylor and Wheelers statement that nothing happens to A as a result of B's actions, it seems more appropriate to say that B's clock is fast, or that B's perception of A's clock is an optical effect, instead of the standard view that all of A's actions are slowed.
The equation relating A and B clocks requires that both be expressed in the same units. With no pre-arrangement, there is no reason that both should use the same, so the adjustment to B's clock is to find A's clock rate in B's units, with the proviso that two light clocks of the same length would read the same time rate, as stated be Feynman. Again, I'm not suggesting absolute time, but time relative between A and B. Then B's clock can be adjusted back to the correct time, but what is the meaning of correct time?
Its very difficult to be clear and precise in a conversatiion such as this, but let's keep trying.